Final answer:
To make a chart from the function 2x^2 + 2x + 1, we can plot the vertex (-0.5, 0.75) and other points such as (0, 1) and (1, 5) to show the parabola's curvature. Using the vertex formula and function evaluation, we can generate and verify points on the graph.
Step-by-step explanation:
To create a chart using the function 2x^2 + 2x + 1, we need to select at least three points, one of which must be the vertex.
- Vertex: (-0.5, 0.75)
- Point B: (0, 1)
- Point C: (1, 5)
Since the given quadratic equation is in the standard form y = ax^2 + bx + c, we can compare it with the general form to identify the coefficients (a=2, b=2, and c=1) and use them to find the vertex.
The vertex can be found using the formula -b/2a for the x-coordinate, and by substituting this value back into the original equation to find the y-coordinate. Now, with the given vertex (-0.5, 0.75), we can create a chart showing this point alongside other selected points such as B (0, 1), and C (1, 5). These points can be plotted on a graph to reveal the shape of the parabola.
Likewise, we can confirm that point D (-1, 3) does not lie on this parabola by substituting x=-1 into the equation. If the corresponding y value does not match, this point would not be included in your chart.